The purpose of this paper is to study certain results concerning the extremal systems of points on the unit sphere \(S^r\subseteq \mathbb{R}^{r+1}\), related to problems of numerical integration and geometrical properties of extremal systems.
The authors consider the worst case cubature error in a certain Hilbert space and its relation to a generalized discrepancy. The minimum geodesic distance between pairs of points and the mesh norm are discussed. They also consider numerical examples.